Determine convergence or divergence of the series.
-$$\sum _ { n = 1 } ^ { \infty } \frac { 6 n ^ { 1 / 3 } } { 6 n ^ { 4 / 3 } + 5 }$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

The series diverges because as $n$ approaches infinity, the dominant term in both the numerator and the denominator is $n^{4/3}$, making the series behave like $\sum \frac{1}{n}$, which is a harmonic series known to diverge.

Determine Convergence or Divergence of the Series ∑n=1∞6n1/36n4/3+5\sum _ { n = 1 } ^ { \infty } \frac { 6 n ^ { 1 / 3 } } { 6 n ^ { 4 / 3 } + 5 }n=1∑∞​6n4/3+56n1/3​

Determine Convergence or Divergence of the Series $\sum _ { n = 1 } ^ { \infty } \frac { 6 n ^ { 1 / 3 } } { 6 n ^ { 4 / 3 } + 5 }$